Yellowstone National Park Coyote facts: The coyote ranges throughout Yellowstone Park frequenting the Firehole, Gibbon and Madison rivers in western Yellowstone, and the Lamar and Hayden valleys at its northeastern tip. Until 1995, the mountain lion was the coyote�s main predator. The reintroduction of the wolf into the park in the mid-1990s however, presented unexpected challenges for the small canine, which suddenly found itself faced with a new predator. Coyote mortality rates within Yellowstone increased until hunting ranges were gradually rearranged by the affected packs and coyote kills began to decline.